Refine your search
Collections
Co-Authors
A B C D E F G H I J K L M N O P Q R S T U V W X Y Z All
Dutta, S.
- On the Class of New Difference Sequence Spaces
Abstract Views :211 |
PDF Views:1
Authors
P. Baliarsingh
1,
S. Dutta
2
Affiliations
1 Department of Mathematics, Trident Academy of Technology, Infocity, Bhubaneswar -751024, IN
2 Department of Mathematics, Utkal University, Vanivihar, Bhubaneswar, IN
1 Department of Mathematics, Trident Academy of Technology, Infocity, Bhubaneswar -751024, IN
2 Department of Mathematics, Utkal University, Vanivihar, Bhubaneswar, IN
Source
The Journal of the Indian Mathematical Society, Vol 80, No 3-4 (2013), Pagination: 203-211Abstract
The main purpose of the present paper is to introduce a new class of difference sequence spaces l∞(Δ[k], ν,p),c0(Δ[k], ν,p) and c(Δ[k], ν,p), where Δ[k](xk) = kxk - (k+1)xk+1 for all k = 1,2,3.... Also, we derive some inclusion relations and other topological properties of these spaces. Finally we discuss about their α-, β-, and γ- duals.Keywords
Difference Sequence Spaces α-, β-, and γ- Duals.
- On Certain Paranormed Difference Sequence Spaces Derived from Generalized Weighted Mean
Abstract Views :237 |
PDF Views:2
Authors
P. Baliarsingh
1,
S. Dutta
2
Affiliations
1 Department of Mathematics, KIIT University, Bhbaneswar 751 024, IN
2 Department of Mathematics, Utkal University, Bhubaneswar 751 004, IN
1 Department of Mathematics, KIIT University, Bhbaneswar 751 024, IN
2 Department of Mathematics, Utkal University, Bhubaneswar 751 004, IN
Source
The Journal of the Indian Mathematical Society, Vol 83, No 1-2 (2016), Pagination: 13-25Abstract
The main objective of the present article is to give a unifying approach to most of the paranormed difference sequence spaces defined in the domain of weighted mean operator. In this work, we introduce certain new paranormed spaces such as l∞(μ, ν; Δr, p), c0(μ, ν; Δr, p), c(μ, ν; Δr, p) and l(μ, ν; Δr, p) by combining the generalized difference operator Δr and the weighted mean operator G(μ, ν). Also we investigate their topological structures and establish their α-, β- and γ- duals. Moreover we characterize the matrix transformations from these spaces to the basic sequence spaces l∞(q), co(q), c(q) and l(q).Keywords
Difference Operator Δr, Generalized Weighted Mean Operator G(μ, ν), Paranormed Difference Sequence Spaces, α, β and γ Duals, Matrix Transformations.References
- Z. U. Ahmad, M. Mursaleen, K¨othe-Toeplitz duals of some new sequence spaces and their martix maps, Publ. Inst. Math. (Beograd), 42(56) (1987), 57–61.
- B. Altay and F. Basar, Some paranormed sequence spaces of non absolute type derived by weighted mean, J. Math. Anal. Appl., 319(2) (2006), 494–508.
- B. Altay, F. Basar, Generalization of sequence spaces ℓ(p) derived by weighted mean, J. Math. Anal. Appl. 330(1) (2007), 174–185.
- C. Asma and R. Colak, On the Kothe-Toeplitz duals of some generalized sets of difference sequences, Demonstratio Math. 33 (2000) 797–803.
- C. Aydın and F. Basar, On the new sequence spaces which include the spaces c0 and c, Hokkaido Math. J., 33 (2004), 383–398.
- C. Aydin and F. Basar, Some new paranormed sequence spaces, Inform. Sci., 160 (2004), 27–40.
- C. Aydin and F. Basar, Some new sequence spaces which include the spaces ℓp and ℓ∞, Demonstratio Math., 38 (2005), 641–655.
- P. Baliarsingh, Some new difference sequence spaces of fractional order and their dual spaces, Appl. Math. Comput., 219(18) (2013), 9737–9742.
- P. Baliarsingh and S. Dutta, On certain new difference sequence spaces generated by infinite matrices, Thai. J. Math., 11(1) (2013), 75–86.
- M. Basarir, On the generalized Riesz B-difference sequence spaces, Filomat, 24(4) (2010), 35–52.
- M. Basarir and E. E. Kara, On some difference sequence spaces of weighted mean and compact operators, Ann. Funct. Anal., 2 (2) (2011), 114–129.
- S. Demiriz, C. Cakan, Some new paranormed difference sequence space and weighted core, Comput. Math. Appl. (in press)
- I. Djolovic, On the spaces of bounded Euler difference sequences and some classes of compact operatos, Appl. Math. Comput., 182 (2006), 1803–1811.
- S. Dutta and P. Baliarsingh, On the fine spectra of the generalized rth difference operator Δrν on the sequence space ℓ1, Appl. Math. Comput., 219(4) (2012), 1776–1784.
- S. Dutta, P. Baliarsingh, On the spectrum of 2-nd order generalized difference operator Δ2 over the sequence space co, Bol. Soc. Paran. Mat., 31(2) (2013), 235–244.
- M. Et and R. Colak, On some generalized difference sequence spaces, Soochow J. Math., 21 (1995), 377–386.
- K. G. Grosse-Erdmann, Matrix transformations between the sequence spaces of Maddox, J. Math. Anal. Appl., 180 (1993), 223–238.
- H. Kızmaz, On Certain Sequence spaces, Canad. Math. Bull., 24 (2) (1981) 169–176.
- I. J. Maddox, Spaces of strongly summable sequences, Quart. J. Math. Oxford, 18(2) (1967), 345–355.
- E. Malkowsky, M. Mursaleen, S. Suantai, The dual spaces of sets of difference sequences of order m and martix transformations, Acta Math. Sin. (English Series), 23(3) (2007),521–532.
- H. Polat, V. Karakaya, N. Simsek, Difference sequence spaces derived by using a generalized weighted mean, Appl. Math. Lett., 24(5) (2011), 608–614.